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Risk apportionment via bivariate stochastic dominance


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  • Jokung, Octave
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    This paper extends to bivariate utility functions, Eeckhoudt et al.’s (2009) result for the combination of ‘bad’ and ‘good’. The decision-maker prefers to get some of the ‘good’ and some of the ‘bad’ to taking a chance on all the ‘good’ or all the ‘bad’ where ‘bad’ is defined via (N,M)-increasing concave order. We generalize the concept of bivariate risk aversion introduced by Richard (1975) to higher orders. Importantly, in the bivariate framework, preference for the lottery [(X̃,T̃);(Ỹ,Z̃)] to the lottery [(X̃,Z̃);(Ỹ,T̃)] when (X̃,Z̃) dominates (Ỹ,T̃) via (N,M)-increasing concave order allows us to assert bivariate risk apportionment of order (N,M) and to extend the concept of risk apportionment defined by Eeckhoudt and Schlesinger (2006).

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 4-5 ()
    Pages: 448-452

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:448-452

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    Keywords: Bivariate utility function; Correlation aversion; Cross-prudence; Cross-temperance; Pair-wise risk aversion; Risk apportionment; Stochastic dominance;


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    1. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, Canadian Economics Association, vol. 13(1), pages 16-34, February.
    2. Louis Eeckhoudt & Harris Schlesinger, 2005. "Putting Risk in its Proper Place," CESifo Working Paper Series, CESifo Group Munich 1462, CESifo Group Munich.
    3. Louis Eeckhoudt & Harris Schlesinger & Ilia Tsetlin, 2008. "Apportioning of Risks via Stochastic Dominance," CESifo Working Paper Series, CESifo Group Munich 2467, CESifo Group Munich.
    4. John Heaton & Deborah Lucas, 2000. "Portfolio Choice and Asset Prices: The Importance of Entrepreneurial Risk," Journal of Finance, American Finance Association, American Finance Association, vol. 55(3), pages 1163-1198, 06.
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    6. Scarsini, Marco, 1985. "Stochastic dominance with pair-wise risk aversion," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 14(2), pages 187-201, April.
    7. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, INFORMS, vol. 52(1), pages 146-153, January.
    8. Scott F. Richard, 1975. "Multivariate Risk Aversion, Utility Independence and Separable Utility Functions," Management Science, INFORMS, INFORMS, vol. 22(1), pages 12-21, September.
    9. Edwards, Ryan D, 2008. "Health Risk and Portfolio Choice," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 26, pages 472-485.
    10. Rosen, H.S.Harvey S. & Wu, Stephen, 2004. "Portfolio choice and health status," Journal of Financial Economics, Elsevier, Elsevier, vol. 72(3), pages 457-484, June.
    11. Menezes, Carmen F. & Wang, X.Henry, 2005. "Increasing outer risk," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 41(7), pages 875-886, November.
    12. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
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    Cited by:
    1. Xue, Minggao & Cheng, Wen, 2013. "Background risk, bivariate risk attitudes, and optimal prevention," Mathematical Social Sciences, Elsevier, Elsevier, vol. 66(3), pages 390-395.
    2. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 49(4), pages 335-343.


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